1. Field of the Invention
The present invention relates to a method for calculating a heating procedure of a linear heating, in which an arrangement and heating conditions for heating lines are determined in order to carry out bending work such as work for a plate into an outer bending plate constituting a vessel shell (work for a metal plate into a target shape of a curved surface) in shipbuilding.
2. Description of the Related Art
In recent years, a method of bending work by a linear heating has been adopted for the bending work for a metal plate for use in a vessel or the like.
The linear heating is a technology of utilizing a property of a metal plate, in which the metal plate generates a plastic strain and deforms itself upon being restricted from a periphery thereof when the metal plate is linearly heated by a point heat source such as a gas burner. In addition, the linear heating is a technology of carrying out bending work for a metal plate as an object into a target shape of a curved surface by arranging heating points on respective spots on a metal plate.
Conventionally, it has been conceived that the bending work for a metal plate by the linear heating is a technique to be acquired through a long-term experience. Heating positions, directions, conditions and the like have been determined by senses and skills of skilled workers, and the bending work has been carried out. However, such a conventional method depending on the work of the skilled workers has involved problems that a long time is required for acquiring the skill and of a lack of successors. Further, a problem of a large variation in working precision has occurred. Therefore, in recent years, a method for mechanically carrying out the linear heating has been proposed.
As this type of method for mechanically carrying out the linear heating, there is a method to be described below. Namely, the surface of a metal plate to be subjected to the bending work is divided into a large number of regions by applying the Finite Element Method (FEM). Moreover, a target specific strain required for executing the bending work into the target shape of a curved surface is obtained for each of the divided regions. Curved heating lines are arranged in a crossing manner on the divided regions of one surface of the metal plate, and the metal plate is locally heated so as to receive a specified supplied heat with a moving velocity of a heat source as a control parameter while moving the heat source along the heating lines. In this manner, the membrane-shrinkage and bending strain components of the target specific strain are given, thereby bending each of the divided regions to the target shape and bending the entire metal plate to a target curved surface.
Note that a plurality of strains (i.e., four strain components including membrane-shrinkage strains along the neutral surface of the plate in two principal axes perpendicular to each other, and bending strains operating to the external direction of the plate surface in the two principal axes perpendicular to each other) are concerned in the bending work for the metal plate by the linear heating.
Meanwhile, strains generated by one heating line includes four components: a membrane-shrinkage strain in the perpendicular direction of the heating line; a membrane-shrinkage strain in the tangential direction of the heating line; a bending strain in the perpendicular direction of the heating line; and a bending strain in the tangential direction of the heating line. These four strain components are determined simultaneously for one heating condition. Therefore, in the case of using a method for heating a plate from one surface thereof by controlling only one control parameter in the above-described moving velocity of the heat source and the like, the four strain components to be obtained cannot be satisfied entirely even if two heating lines are arranged in combination perpendicularly to each other.
Therefore, a method for obtaining a heating procedure has been adopted heretofore, which is realized by: (a) a method for arranging heating lines, disclosed in Japanese Patent Application Laid-Open No. H10-230326; (b) a method for obtaining a membrane strain, disclosed in Japanese Patent Application Laid-Open No. 2001-071041; (c) a method for obtaining a heating condition, in which deformations of a plurality of adjacent heating lines are added together, and four strain components to be obtained from a deformation amount obtained by the addition are obtained averagely and approximately by use of an optimization method and so on; or the like. The above-described Japanese Patent Application Laid-Open No. H10-230326 discloses the method for arranging heating lines by paying attention only to one deformation component affecting the formation of a curved surface most, such as a bending or membrane-shrinkage deformation perpendicular to the heating line, among the four deformation components generated by the heating lines (i.e., bending and membrane-shrinkage deformations in the perpendicular direction of the heating line and bending and membrane-shrinkage deformations in the tangential direction thereof). The above-described Japanese Patent Application Laid-Open No. 2001-071041 discloses the following method including the steps of: dividing a target shape of a curved surface into fine grid regions; assuming a membrane strain in each grid region; obtaining a second-order finite difference approximating second-order differential of membrane strains between a membrane strain in the grid region and a membrane strain in a region surrounding the grid region; forming simultaneous equations on the assumption that the second-order finite difference in the membrane strains and a degree of incompatibility R in a region composed of both the grid region and the region surrounding the same are equal to each other; and determining the membrane strain based on these simultaneous equations. The degree of incompatibility R has already been determined at a point of time when the curved surface was given. The degree of incompatibility R is a value obtained from a distribution of the bending strains or a curvature of the curved surface.
However, the method for arranging a heating line by paying attention only to one component affecting the formation of a curved surface most among four deformation components generated by the heating line has the following problem. Namely, the three remaining deformation components operate as disturbances, whereby a difference between the formed surface and the target shape increases. Accordingly, a case may possibly occur, where a heating condition for approximating the strain distribution giving the target shape of a curved surface precisely is not obtained.
Further, the method for obtaining a heating condition, in which the deformations of the plurality of adjacent heating lines are added together, and four strain components to be determined from the deformation amount given by the addition of the deformations are obtained averagely and approximately by use of an optimization method or the like, has the following problem. That is, magnitudes of deformations given by individual heating lines adjacent to each other are significantly different from each other. Therefore, an extra residual stress is induced around the heating lines, thereby deteriorating local precision of the curved surface.
Moreover, there has been the following problem in the method including the steps of: dividing a target shape of a curved surface into fine grid regions; assuming a membrane strain in each grid region; obtaining a second-order finite difference approximating second-order differentials of membrane strains between a membrane strain in the grid region and a membrane strain in a region surrounding the grid region; forming simultaneous equations on the assumption that the second-order finite difference in the membrane strains and a degree of incompatibility R in a region composed of both the grid region and the region surrounding the same are equal to each other; and obtaining the membrane strain based on these simultaneous equations. The problem is as follows: even if the above-described grid region is arranged along the directions of the two principal axes such that a shearing strain component is not interposed in these simultaneous equations, two independent components that are the bending and membrane strains will exist for each of the directions of the two principal axes, such that the number of unknowns twice the number of equations (i.e., the number of grids) will be included in the equations. Thus, the solution of the simultaneous equations is not determined, so that the following method is forced to be employed: these simultaneous equations are solved on the assumption that the strains equal in aspect each other or that the aspect ratio of the strains is given on the assumption that the aspect ratio has already been known. In this way of obtaining a membrane strain, the target specific strain has been obtained independently of the strain given by the heating line. Therefore, any deformation conforming to the target specific strain does not sometimes exist, such that an extra strain cannot be helped but to be given under the actual situation. Then, this extra strain generates the residual stress. Accordingly, it has been impossible to largely enhance the local precision of the obtained curved surface.
By the way, as means for increasing control parameters, the following method is also disclosed, which includes the steps of: erecting a steel plate vertically; supporting the steel plate by supporting devices arranged on upper and lower ends of the steel plate; arranging heating lines on the front and back surfaces of the steel plate; heating the steel plate by moving heat sources arranged on the front and back surfaces of the metal plate along the heating lines arranged thereon simultaneously in synchronization with each other; and obtaining four strain components (see Japanese Patent Application Laid-Open No. H10-146620). As the control parameters, two are set: the moving velocity of the heat source; and the outputs of the heat sources on the front and back surfaces, and thus the four strain components are precisely obtained. However, in this case, there are required: (a) a heating apparatus capable of controlling the heat sources simultaneously in synchronization with each other on both of the front and back surfaces of the steel plate; and (b) large equipments such as devices supporting the steel plate arranged in the vertical direction. Therefore, a heating procedure has been desired, which enables to realize a more accurate target shape of a curved surface by controlling only one control parameter.
In this connection, it is an object of the present invention to provide a method for calculating a heating procedure of a linear heating, which is prepared for realizing a target shape of a curved surface accurately with precision sufficient for practical use even if a supplied heat is controlled only by one control parameter.
The first aspect of the present invention provides a method for calculating a heating procedure of a linear heating, the method comprising the steps of: determining a distribution of bending principal strains for giving a target shape of a curved surface; dividing calculation grids along directions of the bending principal strains; dividing the directions of the bending principal strains into both a direction of a maximum bending principal strain and a direction of a minimum bending principal strain for each of the calculation grids; determining a heating condition for heating a plurality of heating lines perpendicular to the direction of the maximum bending principal strain, the heating condition defying the maximum bending principal strain; obtaining membrane strains generated accompanying with heating the plurality of heating lines under the heating condition from a database, the database including a relation between the heating condition and deformation components; calculating a distribution of membrane strains required for achieving a deflection of the target shape of the curved surface in consideration of a distribution of the membrane strains obtained from the database; selecting a heating condition satisfying both the maximum bending principal strain and the calculated distribution of the membrane strains; and determining a heating procedure under the selected heating condition.
According to the first aspect of the present invention, it is confirmed that, when the linear heating is executed according to the obtained heating procedure, a heating condition for heating lines perpendicular to the direction of the maximum bending principal strain exists in a database, the heating lines being prepared for realizing a bending deformation to the target shape of a curved surface in the direction of the maximum bending principal strain. Therefore, a bending deformation conforming to the requirement is executed without fail. Meanwhile, a heating condition that satisfies membrane strains required for realizing a deflection of the target shape of a curved surface is selected for the heating lines in the direction of the maximum bending principal strain. Thus, the membrane strains in two principal axis directions are realized precisely. Therefore, the maximum bending principal strain and the membrane strains in the two principal axis directions are realized accurately. Accordingly, even if the minimum bending principal strain hardly affecting the formation of the curved surface is ignored, the bending work is executed with high precision sufficient for practical use.
The second aspect of the present invention provides a method for calculating a heating procedure of a linear heating, the method comprising the steps of: determining a distribution of bending principal strains for giving a target shape of a curved surface; dividing calculation grids along directions of the bending principal strains; dividing the directions of the bending principal strains into both a direction of a maximum bending principal strain and a direction of a minimum bending principal strain for each of the calculation grids; determining a heating condition for heating a plurality of heating lines perpendicular to the direction of the maximum bending principal strain, the heating condition defying the maximum bending principal strain; obtaining membrane strains generated accompanying with heating the plurality of heating lines under the heating condition from a database, the database including a relation between the heating condition and deformation components; calculating a distribution of membrane strains required for achieving a deflection of the target shape of the curved surface in consideration of a distribution of the membrane strains obtained from the database; setting the plurality of heating lines along the direction of the maximum bending principal strain as one set, the plurality of heating lines being perpendicular to the direction of the minimum bending principal strain, and the one set of the plurality of heating lines being arranged parallel one another at a specified interval; obtaining a heating condition for each of the plurality of heating lines such that a sum of the deformation components generated by heating each of the plurality of heating lines allows to give the minimum bending principal strain and the calculated distribution of membrane strains required for achieving a deflection of the target shape of the curved surface; and determining a heating procedure satisfying the maximum principal strain, the minimum bending principal strain and the membrane strains under the obtained heating condition.
According to the second aspect of the present invention, the linear heating is executed in accordance with the obtained heating procedure, whereby all of the maximum and minimum bending principal strains and the membrane strains in the two principal axis directions can be realized accurately. Furthermore, the bending work can be executed with high precision. Consequently, even if the curved surface is twisted largely and asymmetric, in which the bending principal strains in the two principal axis directions are required to be combined accurately with each other, and if the membrane shrinkage is required to be accurately given around the approximate center of the steel plate, the bending work can be executed therefor precisely.
The third aspect of the present invention provides the method for calculating a heating procedure of a linear heating according to the second aspect of this invention, wherein, when a plurality of heating lines perpendicular to the direction of the minimum bending principal strain are set as the one set and disposed parallel at the specified interval, each the one set of the heating lines is arranged separately on front and back surfaces of a steel plate as a material.
According to the third aspect of the present invention, the bending components of the deformations obtained by the heating of one set of the heating lines are canceled with each other, and the sum of the bending components is reduced. Therefore, the heating procedure can be made effective when the membrane shrinkage is large and the bending deformation is small in the required deformation.
The fourth aspect of the present invention provides the method for calculating a heating procedure of a linear heating according to the second aspect of this invention, wherein, when the plurality of heating lines perpendicular to the direction of the minimum bending principal strain are set as the one set and disposed parallel at the specified interval, a width of each of the calculation grids along the direction of the minimum bending principal strain is set, and an absolute amount of the sum of the deformation components, which is generated by heating each of the one set of the heating lines, equals a required deformation amount different for each of the calculation grids located along the direction of the maximum bending principal strain.
According to the fourth aspect of the present invention, the absolute amount of the sum of the generated deformation components can be freely controlled while the ratio of the bending deformation and the membrane deformation is kept at a ratio required for forming the curved surface of the relevant portion. Moreover, while required deformation amounts are satisfied accurately, the required deformation amounts being different from one another in calculation grids arrayed in the direction of the maximum bending principal strain, sets of a plurality of the heating lines can be arranged continuously.
The fifth aspect of the present invention provides the method for calculating a heating procedure of a linear heating according to the first and second aspects of this invention, wherein a heating velocity is adopted as the heating condition, and the database is configured by storing actual measurement values showing relations between the heating velocity and the deformation components.
According to the fifth aspect of the present invention, as the control parameter, the heating velocity can be employed, which is generally used as a control parameter when executing the linear heating.
The sixth aspect of the present invention provides the method for calculating a heating procedure of a linear heating according to the first and second aspects of this invention, wherein a supplied heat is adopted as the heating condition, and the database is configured by storing actual measurement values showing relations between the supplied heat and the deformation components.
According to the sixth aspect of the present invention, as the control parameter, the supplied heat can be employed, which is generally used as a control parameter when executing the linear heating.